Is boundary conformal in CFT?

Abstract

We discuss boundary conditions for conformal field theories that preserve the boundary Poincare invariance. As in the bulk field theories, a question arises whether boundary scale invariance leads to boundary conformal invariance. With unitarity, Cardy's condition of vanishing momentum flow is necessary for the boundary conformal invariance, but it is not sufficient in general. We show both a proof and a counterexample of the enhancement of boundary conformal invariance in (1+1) dimension, which depends on the extra assumption we make. In (1+2) dimension, Cardy's condition is shown to be sufficient. In higher dimensions, we give a perturbative argument in favor of the enhancement based on the boundary g-theorem. With the help of the holographic dual recently proposed, we show a holographic proof of the boundary conformal invariance under the assumption of the boundary strict null energy condition, which also gives a sufficient condition for the strong boundary g-theorem.

30 pages, v2: references and comments added v3: minor corrections, to be published

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• Bending branes for DCFT in two dimensions
• Colliders and conformal interfaces
• Scale invariance vs conformal invariance
• The Conformal Anomaly in bCFT from Momentum Space Perspective
• Line defects in the 3d Ising model
• Zoology of heterotic supercurrent supermultiplets in d=2
• Disclinations, dislocations, and emanant flux at Dirac criticality
• (0,2) Chiral Liouville Field Theory
• Boundary Conformal Field Theory at Large Charge
• Scale without Conformal Invariance in bottom-up Holography